Jason jumped off a cliff into the ocean while vacationing with some friends. His height as a function of time could be modeled by the function h(t)= -16t^2 + 16t + 480, where t is the time in seconds and h is the height is feet.
a. How long did it take for Jason to reach his maximum height?
The time to reach the max height is given by :
-16/ [ 2 * -16] = 1 / 2 sec
b. What was the highest point that Jason reached?
Highest point = -16(1/2)^2 + 16 (1/2) + 480 = -4 + 8 + 480 = 484 ft
c. Jason hit the water after how many seconds?
We need to solve this :
-16t^2 + 16t + 480 = 0 divide throug by - 16
t^2 - t - 30 = 0 factor
(t + 5) ( t - 6) = 0
Seteting each factor to 0 and solving for t produces
t = - 5 sec [ reject ]
or
t = 6 sec [ accept ]
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